Big asked in Science & MathematicsMathematics · 7 years ago

# Solve the following Linear Programming Problem via the Simplex Method:?

Help!! I need to know what the inequalities/equations are to set up this problem:

Solve the following Linear Programming Problem via the Simplex Method:

A city council is working with a hotel developer to build several hotels along its beach-front.

The developer has three prototypes: a convention-style hotel with 500 rooms costing \$100 million, a vacation-style hotel with 200 rooms costing \$20 million, and a small hotel with 50 rooms costing \$4 million.

The city council wants a total capacity of at least 3,000 rooms and has three other restrictions:

• at most three convention-style hotels;

• at most twice as many small hotels as vacation-style; and

• at least a fifth as many convention-style hotels as vacation-style and small combined.

How many hotels of each type should the council request in order to minimize cost?

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• 7 years ago

Big Hi!

Solve the following Linear Programming Problem via the Simplex Method:?

Help!! I need to know what the inequalities/equations are to set up this problem:

Solve the following Linear Programming Problem via the Simplex Method:

A city council is working with a hotel developer to build several hotels along its beach-front.

The developer has three prototypes: a convention-style hotel with 500 rooms costing \$100 million, a vacation-style hotel with 200 rooms costing \$20 million, and a small hotel with 50 rooms costing \$4 million.

The city council wants a total capacity of at least 3,000 rooms and has three other restrictions:

• at most three convention-style hotels;

• at most twice as many small hotels as vacation-style; and

• at least a fifth as many convention-style hotels as vacation-style and small combined.

How many hotels of each type should the council request in order to minimize cost?

Let C = Convention-style Hotel → 500 rm costing \$ 100 Million

V = vacation-style hotel → 200 rm \$ 20 million

S = small hotel → 50 \$ 4 million

CONDITIONS:

1. Capacity = 3,000 rooms

2. C ≤ 3

3. S = 2V

4. C = 1/5 (V + S)

C + V + S = 3000 ← eq5

C = 3 ◄ No. of Convention Hotels

From 4

C = 1/5 (V + S)

3 = 1/5 (V + 2V)

15 = 3V

==================================

V = 5 ◄ No. of Vacation-style Hotels

==================================

Substitute V to 3

S = 2(5)

==============================

S = 10 ◄ No. of Small Hotels

==============================

From eq5

C + V + S = 3000

3(500) + 5(200) + 10(50) = 3000

1500 + 1000 + 500 = 3000

3000 = 3000 ← Correct

Cost

C = 3 (100 m ) → \$ 300 m

V = 5 (20 m ) → \$ 100 m

S = 10 (4 m ) → \$ 40 m

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Total → \$ 440 million

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Hope this helps

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